The state-of-the-art fiber-optics communication systems standardized by the ITU employ different concatenated Bose-Chaudhuri-Hocquenghem (BCH)/Reed-Solomon (RS) codes. Recently, iteratively decodable codes, turbo and low-density parity-check (LDPC) code, have generated significant research attention. It has been shown that turbo product codes (TPCs) can be matched and outperformed by LDPC codes in terms of coding gain and decoding complexity. Generalized low-density parity-check (GLDPC) coding can further improve the overall characteristics of LDPC codes by decreasing the complexity of the decoder, which is of high importance for optical communications. The main idea behind the GLDPC codes is to replace the parity-check equations in a parity-check matrix of global LDPC code by a linear block code. The decoding is based on a combination of simple and fast soft-input-soft-output (SISO) linear block decoders operating in parallel. The bit reliabilities obtained by SISO decoders are passed to the message-passing decoder operating on a bipartite graph of a global LDPC code. The SISO decoders are commonly designed as maximum a posteriori probability (MAP) decoders, such as Bahl-Cocke-Jelinek-Raviv (BCJR) decoder, and provide accurate estimates of bit reliabilities for a global LDPC decoder after small number of iterations. Due to high-complexity of the BCJR decoder, the GLDPC coding is limited to simple linear block component codes such as Hamming codes.
Accordingly, there is a need for generalized low-density parity-check code GLDPC encoding that provides excellent coding gains while low-complexity decoding.